A Large Consulting Firm Is Deciding on If Its Workforce

A large consulting firm is deciding on if its workforce should be expanded, maintained, or decreased. Suppose that demand is given in week long projects, and that a consultant can work on 3 projects each month (1 week off for personal leave and/or other duties such as conferences, etc). Currently there are 25 consultants. Ten consultants are trained for LEAN and 15 for Six Sigma, with 5 of those consultants being overlaps (the consultant is trained for BOTH LEAN and Six Sigma). Assume that all consultants can do the general work. Complete the table (the forecast period is an upcoming month) and prepare a recommendation.
$$\begin{array} { | l | c | c | c | c | c | } \hline \text { Category } & \begin{array} { c } \text { Best } \\\text { Forecast } \\\text { (\# } \\\text { projects) }\end{array} & \begin{array} { c } \text { Likely } \\\text { Forecast } \\\text { (\# } \\\text { projects) }\end{array} & \begin{array} { c } \text { Worst } \\\text { Forecast } \\\text { (\# } \\\text { projects) }\end{array} & \begin{array} { c } \text { Maxand in } \\\text { \# of } \\\text { people }\end{array} & \begin{array} { c } \text { Number of } \\\text { Qualified } \\\text { People }\end{array} \\\hline \text { LEAN } & 42 & 24 & 12 & & \\\hline \text { Six Sigma } & 45 & 36 & 30 & & \\\hline \text { General } & 75 & 60 & 57 & & \\\hline\end{array}$$